Sonar broadband constant beamwidth shading network

ABSTRACT

A beamwidth shading network disposed between a beamformer and the point at which the delayed inputs are summed or the point at which the beam is formed, which includes for each hydrophone in the array a multiplier, a compensating delay and a transverseal filter. The transversal filters provide a weighting function for the associated input so that, with the proper weighting function applied, the beam is shaded and forms an essentially rectangular beam pattern for a line array over a broadband of frequencies.

Muted States Patent [191 Autrey Dec.3,i974

[ SONAR BROADBAND CONSTANT BEAMWIDTH SHADING NETWORK [75] Inventor: Samuel W. Autrey, Fullerton, Calif.

[73] Assignee: The United States of America as represented by the Secretary of the Navy, Washington, DC.

22 Filed: Feb. 23, 1968 21 Appl. No.1 707,595

[52] U.S. Cl. 340/6 R, 340/6 S [51] Int. Cl. G015 3/80 [58] Field of Search 340/6, 6 S, 16, 9

[56] References Cited UNITED STATES PATENTS 3,412,372 11/1968 Ladstatter 340/6 Mum/ un? 13 77 Primary ExaminerRichard A. Farley Attorney, Agent, or Firm-Richard S. Sciascia; Arthur A. McGill; Prithvi C. Lall 5 7 ABSTRACT A beamwidth shading network disposed between a beamformer and the point at which the delayed inputs are summed or the point at which the beam is formed, which includes for each hydrophone in the array a multiplier, a compensating delay and a transverseal filter. The transversal filters provide a weighting function for the associated input so that, with the proper weighting function applied, the beam is shaded and forms an essentially rectangular beam pattern for a line array over a broadband of frequencies.

3 Claims, 14 Drawing Figures N MP5 (IV-f) T PATENTEL BEE 31974 INPUT Maw/PL lgg INVENTOR. W. 191/7257 SONAR BROADBAND CONSTANT BEAMWIDTH SHADING NETWORK BACKGROUND OF THE INVENTION to provide a rectangular beam over an extended frel quency range.

2. Description of the Prior Art Many investigators have dealt with the problem of achieving a specified beam pattern with a line array, basing their syntheses on the Fourier series nature of the patterns obtained with equally spaced array elements, or using the Fourier transform pair relationship of the beam pattern and the illumination in continuous arrays. These and later works have generally been of a theoretical nature with the design frequency fixed; i.e., implicit single frequency studies.

When the braodband problem is studied the theoretical aspects of the Fourier transform pair are invariably overlooked in favor of apparent and attractive approximating techniques. In one such technique a broad beam is generated by summing a large number of beams steered to different directions. In its simplest form the scheme yields beamwidths that are not constant with frequency, but with modifications equivalent to varying the steering angles of the constituent beams as functions of frequency, the summed beamwidth can be maintained approximately constant over several octaves. The formed beams must be properly delayed before summation in order to relate them all to the same reference, i.e., they must appearto have been formed from arrays with coincident phase centers. In other approaches the same basic idea was implemented theoretically with a number of line arrays all lying in the same plane and having the same midpoint. This technique was then extended to the formation of beams essentially constant in width in two dimensions with a twisted planar array.

Other techniques include shaping the surface of the transducer to produce the desired pattern directly (which is actually what is done with the twisted planar array), varying the effective aperture as with low pass filters or a multiplicity of resonant arrays, but apart from the twisted array they have not been pursued to any successful conconslusions.

SUMMARY OF INVENTION The general purpose of this invention is to provide a broadband constant beamwidth radiation pattern through the employment of various shading networks. The present invention provides a unique frequency selective network for each hydrophone, which network includes a multiplier, a delay and a transversal filter having a specific number of tapped delays.

An object of the present invention is to provide a beam forming network that permits any array factor vs. azimuth vs. frequency characteristics with an arbitrarily close approximation.

Another object is to provide a beam forming network in which the beam patterns are directly synthesized and digital circuitry can be employed.

BRIEF DESCRIPTION OF THE DRAWINGS Other objects and many of the attendant advantages of this invention will be readily appreciated as the same becomes better understood by reference to the following detailed description when considered in connection with the accompanying drawings, in which like reference numerals designate like parts, wherein:

FIG. 1 is a block diagram of an ideal array shading 0 network;

FIGS. 2(a), 2(b), 2(c) and 2(d) are graphic illustrations of frequency dependent hydrophone weighting functions;

FIGS. 3(a), 3(b) and 3(0) illustrate the beam patterns resulting from various weighting functions;

FIG. 4 is a block diagram of a simplified weighting network;

FIG. 5 is a block diagram representing a shading network for providing constant bandwidth;

FIG. 6 is a graphical plot of the beam pattern attained for an array employing the shading network of FIG. 5;

FIG. 7 is a plot of the angular variable of FIG. 6; FIG. 8 is a block diagram of a typical transversal filter showing the various tap values; and,

FIG. 9 is a graph of weighting functions for two specific hydrophones.

DESCRIPTION OF A PREFERRED EMBODIMENT In the application of hydrophone line arrays in underwater sound programs, it has become increasingly important to control the beam patterns over broad (percentage) bands of frequency. One beam pattern having application to many problem areas is that in which the beam width is maintained essentially constant over a broadband. It should be noted that the shading network affects only the beam pattern and not the direction in which the beam is steered. Steering is performed by progressively delaying the hydrophone outputs so that they all add in phase for sound waves from the preferred direction. This steering, or progressive delay of the inputs, takes place in the beamformer, which may form a large number of beams either simultaneously or sequentially. The shading network usually lies between the beamformer and the point at which the delayed inputs are summed, i.e., the point at which the beam is actually formed. The array geometry and the shading I network determine the beam pattern.

Since the beam pattern and the illumination (or element weighting for discrete sensors) constitute a Fourier transform pair, maintaininga constant beam pattern as a function of frequency requires that the illumination be constant as a function of frequency, i.e., that the array aperture in wavelengths and the relative weighting over that aperture be constant with frequency. Since the physical dimensions of the array are not frequency dependent, the effective physical length must be made to vary inversely with frequency to maintain an essentially constant aperture in wavelengths. This must be accomplished with the element weighting networks that constitute the array shading network. Thus, at low frequencies all of the array elements must contribute substantially to the summed beam, but as the frequency increases those elements near the end of the array must contribute less and less to the sum. At the highest frequency of interest, only those elements crease with frequency to reduce the effective physical length of the array with frequency. As an example, suppose the array is made symmetrical about the midpoint and that the element weighting functions are as given by equation (1) below:

NU -ntfl Sin ("7rf1')/7mf'r Some of these frequency dependent hydrophone weighting functions are illustrated in FIG. 2 and with this shading network, the array output, Sffitll), is readily determined as the sum of the weighted hydrophone outputs. This summation is most easily evaluated in terms of the progressive phase shift between input signals, 4:.

l flf i II cud/c sin 41 Here d is the hydrophone spacing, c is the velocity of propagation, ill is the energy arrival angle, and f,, is the frequency for which the spacing is one-half wavelength. Evaluation of the sum is greatly simplified when all phase shifts are referenced to that of the center hydrophone.

i G,,(f) cos ml! (4) N sin (mi-fr) cos nil! N sin (mrfr) This is recognized as the first N+l terms of the Fou-- rier series expansion of the function shown in FIG. 3a, which has a period of 211.

FIG. 3b follows from FIG. 3a by substituting (sin J M/f. for r and dividing the variable and the absissa by vrf/fl FIG. 3b results from a further change of scale.

Thus, the weighting functions of equations (1) and FIG. 2 result in the beam pattern of FIG. 30 if an infinite number of array elements are usednWith a finite number of elements, the beam pattern will be essentially as shown but contain ripples. Note that the amplitude of the beam output is inversely proportional to frequency. This has no effect on the pattern and may readily be compensated, e.g., by following the shading network with a single RC network.

The required frequency functions may be approximated by networks such as that of FIG. 4, which is simply a delay line 13 with n-l sections. The output must be normalized to unity by multiplying by 1/" at multiplier 14; otherwise, the n taps of unity weighting result in an output of magnitude n.

This summation carried out at 15 results in a delay equal to that at the midpoint and a magnitude characteristics, I-I,,(/).

Alternatively, H U), could have been expressed in a manner to exhibit its Fourier series nature. For in odd:

Thus, the H,,(f) realized with the simple tapped delay line yields a very good approximation to the required weighting functions, the GM). For fr less than 0.25, the error .is less than 10 percent. Thus, since 'r sin lb /fd, the error is less than 10 percent for siml; 0.25 at the design frequency of the array, i.e., f=f,,.

Hence, a very good approximation to a constant beamwidth over a broadband of frequencies is achieved with the shading network of FIG. 5. Note that the normalizing factor [/11 where n is the input terminal designation for 2N+l hydrophones is applied at each input, by the multiplier 13' as is the delay l6"'required to compensate for the different lengths of the tapped delay lines. The latter have been labeled transversal filters 14", since this is their common name in such applications.

Considering an array having 50 hydrophones with a half wavelength spacing frequency of f,,. The wide beam characteristics desired are constant response i0.5 db from 11 /8 to 1.5 fi i.e., I211, for four different beam widths, hereafter called beam factors of 3.8, 6.2", 8.2 and l4.2.

In this approach all of the tap points of the transversal filters were given equal weights yielding a sin x/x frequency characteristics, but it is clear that any arbitrary frequency characteristic may be approximated as closely as is desired by letting the taps have different weightings, and the resulting transmission will be a Fourier series in frequency, as in equation (ll) in which all of the coefficients are two, leading to tap val- 1+2 cos (Zknf'r) 5 6 ues of unity. This may lead to very long delay lines, as shown in FIG. 8. An identical network is also used however, and large numbers of taps for accurate reprefor hydrophone number 33. sentation of complex functions. In any event, the imple- The required multiplications are achieved in a resismentation is simplified and made more accurate when tor matrix; voltage sources at the tap points drive the delay lines are made digital in nature. This requires 5 through this matrix to four low impedance summing that the inputs be characterized by one-bit pulse trains. points, where the four beams are formed, just as the Thus, they may be infinitely clipped, and all of the opsingle beam was formed in FIG. 5. The delay prior to erations remain linear for the signals in the low S/N the first tap used is the seven blocks of delay in which ratio case,-or they may be delta modulated, in which the unused taps 1 through 7 reside. case all of the operations commute with the demodulai 9 Shows the weighting function desired for tion process, so they may be thought of as operating on dFOPhOYIBS number 13 and 33 for the 14.2 beam analog signals. The latter approach, with th t t factor only and the functions actually achieved with beamwidth equipment, is described h i the two networks designed as in FIG. 8. This is the mea- A more hi i d b pattern approximation sured transmission from the input to the output of P10. was also made in the design actually implemented. in i The Sigheis were delta thodhiated with a iPi P h foregoing paragraphs a d i was postulated and riod of r/16; thus, the taps were located at 16-bit interh l d it i now clear h hi design Could vals on the shift register that constituted the delay line. have been synthesized by making a Fourier series exh the actual i heh h t the y p e pansion of the desired beam pattern (FIG. 3c) to deter- Sighais time division mhitiPhed a P Q mine the required weighting f ti (FIG 2 and 20 delay lines and gated off at appropriate times. This equation (1)), and then those weighting functions strategem was employed sihipiy e take advantage of mid have been Synthesized by making Fourier Series the large numbers of bits available in small packages of approximations to them (equation (1 1)), and then the Shift registersthose approximations could be realized in transversal The tap values were computed e used to compute filters (FIG the outputs of the complete shading network for each The beam pattern B (I) (15) is Shown in FIG. It of the four beam factors as functions of azimuth and is constant out to i #0 and Zero beyond 1 +21) Po, the frequency. The amplitude in the main lobe was genertransition region is spanned by two parabolic sections any Constant to within db over the frequency 16, 17, and the slope is continuous throughout the enrange ffomfdlg to 15 About 15 percent fi tire i mew a1 beamwidth was noted for the broadest beam, the varia- The Fourier Series expansion PM), of BM) for an tion being higher for the'narrow beams because the aperture is not large enough to yield the narrower beams ne i he s l even number of array elements is Obtai d nt u ua at the lower frequencies. The maximum theoretical Hen each hydr hon st b i ht d b a i sidelobes for the narrow beam factors range from -13 x/x -[(sin y)/(y)] function or frequency. These funcdb at the lower band edge through about -27 db at the tions were obtained by Fourier series approximations geometric midfreqhehey to about 33 db at the PP arbitrarily limited to a dc term and 12 harmonics in band edge- For the bread beam teeters, the Sideiehe order that circuit boards could be readily fabricated. lt Structure were gehetaiiy ever 24 db dewh- Measured developed that this restriction limited the accuracy of data agree weii with the theetetieai Performance, with the approximation for the 14 beam, and it was found broadband Sideiebes geheraiiy Over 20 db down from necessary to permit k of equation (12), i.e., the transit main lobetion width, to vary as a function of frequency to mainit will be understood that various changes in the detain good beam patterns. A plot of k versus 111 is given tails, materials, and arrangements of parts (and steps), in FIG. 7, following the summary. which have been'herein described and illustrated in The coefficients of the Fourier series expansions of order to explain'the nature of the invention, may be the weighting functions were determined, i.e., the made by those skilled in the art. transversal filter tap values. The resulting tap values lclaimz. I

were rounded off, and all taps less than 5 percent of the 1 a li eqnispaeed h d bh array of 2N+i maximum tap on any single filter were set equal to zero. h d h connected to a b f a b idth The hydrophones are numbered 1 a eae e of the shading network disposed between said beamformer array and 25 at the middle; the maximum tap value cold a um in n t ork which compri es;

umn corresponds to the multipliers prece ing the an input terminal for each outputof said beamfonner delaylines'of FIG. 5; and the design tau corresponds to corresponding t on of said hydroph n s, said that Of FIG. 3, but with a different scale factor. The acinput for the center reference hydrophone being tual delay between taps is the same for all four beam d ignated a Q and each of s id termin ls b ing factors and is determined by the frequency interval d i d b h number of terminals e b over which the weighting functions are approximated, twe n in l ding said refer n terminal, th d dc to 1.5 f,,, and hence, is 1/(3fd). Thus, each hydroterminals being designated N,

phone has one delay line (actually a shift register) with a linear series connected signal path for each of said four sets of taps, one for each beam factor. As an examinput terminals which includes,

ple, the transversal filter for hydrophones number 18 is a multiplier having a factor 1/n, where n designates '7 8 said input terminal except said center terminal said tap outputs connected to the input of said sumhaving a factor of unity, ming network. a compensating delay of (N n) /2)-r, where 1- 2. The network according to claim 1 wherein said linsine of the energy arrival angle divided by the freear d l means i a hif register,

quency for which the spacing of adjacent hydro- 5 phones is one-half wavelength,

a linear delay means having a total delay of (n-1 )r ear delay means is a transversal filter and :1 equal tap outputs,

3. The network according to claim 1 wherein said lin- 

1. In a linear equispaced hydrophone array of 2N+1 hydrophones connected to a beamformer, a beamwidth shading network disposed between said beamformer and a summing network which comprises: an input terminal for each output of said beamformer corresponding to one of said hydrophones, said input for the center reference hydrophone being designated as ''''O'''' and each of said terminals being designated by the number of terminals therebetween including said reference terminal, the end terminals being designated N, a linear series connected signal path for each of said input terminals which includes, a multiplier having a factor 1/n, where n designates said input terminal except said center terminal having a factor of unity, a compensating delay of ( (N-n) /2) Tau , where Tau sine of the energy arrival angle divided by the frequency for which the spacing of adjacent hydrophones is one-half wavelength, a linear delay means having a total delay of (n-1) Tau and n equal tap outputs, said tap outputs connected to the input of said summing network.
 2. The network according to claim 1 wherein said linear delay means is a shift register.
 3. The network according to claim 1 wherein said linear delay means is a transversal filter. 